A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of –0.004 cm, the correct diameter of the ball is

A physical quantity of the dimensions of length that can be formed out of c, G and $${{{e^2}} \over {4\pi {\varepsilon _0}}}$$ is [c is velocity of light, G is the universal constant of gravitation and e is charge]

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitional constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length ?

If dimensions of critical velocity $$\upsilon $$_c of a liquid flowing through a tube are expressed as $$\left[ {{\eta ^x}{\rho ^y}{r^z}} \right]$$ where $$\eta ,\rho $$ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by